A theory of synaptic transmission.

Rapid and precise neuronal communication is enabled through a highly synchronous release of signaling molecules neurotransmitters within just milliseconds of the action potential. Yet neurotransmitter release lacks a theoretical framework that is both phenomenologically accurate and mechanistically realistic. Here, we present an analytic theory of the action-potential-triggered neurotransmitter release at the chemical synapse.

Chromosome dynamics near the sol-gel phase transition dictate the timing of remote genomic interactions.

Diverse antibody repertoires are generated through remote genomic interactions involving immunoglobulin variable (V), diversity (D) and joining (J) gene segments. How such interactions are orchestrated remains unknown. Here we develop a strategy to track V-DJ motion in B-lymphocytes.

Distinguishing Signatures of Multipathway Conformational Transitions.

The folding and binding of biomolecules into functional conformations are thought to be commonly mediated by multiple pathways rather than a unique route. Yet even in experiments where one can "see" individual conformational transitions, their stochastic nature generally precludes one from determining whether the transitions occurred through one or multiple pathways. We establish model-free, observable signatures in the response of macromolecules to force that unambiguously identify multiple pathways-even when the pathways themselves cannot be resolved.

First-Passage Processes in the Genome.

Many essential processes in biology share a common fundamental step-establishing physical contact between distant segments of DNA. How fast this step is accomplished sets the "speed limit" for the larger-scale processes it enables, whether the process is antibody production by the immune system or tissue differentiation in a developing embryo. This naturally leads us to ask, How long does it take for DNA segments that are strung out over millions of base pairs along the chromatin fiber to find each other in the crowded cell? This question, fundamental to biology, can be recognized as the physics problem of the first-passage time, or the waiting time for the first encounter.

Decoding the mechanical fingerprints of biomolecules.

The capacity of biological macromolecules to act as exceedingly sophisticated and highly efficient cellular machines - switches, assembly factors, pumps, or motors - is realized through their conformational transitions, that is, their folding into distinct shapes and selective binding to other molecules. Conformational transitions can be induced, monitored, and manipulated by pulling individual macromolecules apart with an applied force. Pulling experiments reveal, for a given biomolecule, the relationship between applied force and molecular extension.

Statistical mechanics of viral entry.

Viruses that have lipid-membrane envelopes infect cells by fusing with the cell membrane to release viral genes. Membrane fusion is known to be hindered by high kinetic barriers associated with drastic structural rearrangements-yet viral infection, which occurs by fusion, proceeds on remarkably short time scales. Here, we present a quantitative framework that captures the principles behind the invasion strategy shared by all enveloped viruses.

3D trajectories adopted by coding and regulatory DNA elements: first-passage times for genomic interactions.

During B lymphocyte development, immunoglobulin heavy-chain variable (VH), diversity (DH), and joining (JH) segments assemble to generate a diverse antigen receptor repertoire. Here, we have marked the distal VH and DH-JH-Eμ regions with Tet-operator binding sites and traced their 3D trajectories in pro-B cells transduced with a retrovirus encoding Tet-repressor-EGFP. We found that these elements displayed fractional Langevin motion (fLm) due to the viscoelastic hindrance from the surrounding network of proteins and chromatin fibers.

Conformational dynamics through an intermediate.

The self-assembly of biological and synthetic nanostructures commonly proceeds via intermediate states. In living systems in particular, the intermediates have the capacity to tilt the balance between functional and potentially fatal behavior. This work develops a statistical mechanical treatment of conformational dynamics through an intermediate under a variable force.

Kinetics and energetics of biomolecular folding and binding.

The ability of biomolecules to fold and to bind to other molecules is fundamental to virtually every living process. Advanced experimental techniques can now reveal how single biomolecules fold or bind against mechanical force, with the force serving as both the regulator and the probe of folding and binding transitions. Here, we present analytical expressions suitable for fitting the major experimental outputs from such experiments to enable their analysis and interpretation.

A transformation for the mechanical fingerprints of complex biomolecular interactions.

Biological processes are carried out through molecular conformational transitions, ranging from the structural changes within biomolecules to the formation of macromolecular complexes and the associations between the complexes themselves. These transitions cover a vast range of timescales and are governed by a tangled network of molecular interactions. The resulting hierarchy of interactions, in turn, becomes encoded in the experimentally measurable "mechanical fingerprints" of the biomolecules, their force-extension curves.

Single molecules in an extension clamp: extracting rates and activation barriers.

When a macromolecule, held at a fixed end-to-end separation, undergoes conformational rearrangements, the fluctuating mechanical force generated by the molecule can be used as a reporter of the molecular conformational dynamics. We present an analytical framework for extracting the intrinsic rates of conformational transitions and the locations and heights of the rate-limiting barriers from such extension clamp measurements. The unique nature of the bias imposed by the extension clamp on the activation barriers allows access to biomolecular transitions currently not accessible in pulling experiments.

Locating the barrier for folding of single molecules under an external force.

Single-molecule pulling experiments on the folding of biomolecules are usually interpreted with one-dimensional models in which the dynamics occurs on the "pulling coordinate." Paradoxically, the free-energy profile along this coordinate may lack a refolding barrier, yet a barrier is known to exist for folding; thus, it has been argued that pulling experiments do not probe folding. Here, we show that transitions monitored in pulling experiments probe the true folding barrier but that the barrier may be hidden in the projection onto the pulling coordinate.

Biomolecules under mechanical stress: a simple mechanism of complex behavior.

The unfolding of a biomolecule by stretching force is commonly treated theoretically as one-dimensional dynamics along the reaction coordinate coincident with the direction of pulling. Here we explore a situation, particularly relevant to complex biomolecules, when the pulling direction alone is not an adequate reaction coordinate for the unfolding or rupture process. We show that in this case the system can respond to pulling force in unusual ways.

Nanopore force spectroscopy tools for analyzing single biomolecular complexes.

The time-dependent response of individual biomolecular complexes to an applied force can reveal their mechanical properties, interactions with other biomolecules, and self-interactions. In the past decade, a number of single-molecule methods have been developed and applied to a broad range of biological systems, such as nucleic acid complexes, enzymes and proteins in the skeletal and cardiac muscle sarcomere. Nanopore force spectroscopy (NFS) is an emerging single-molecule method, which takes advantage of the native electrical charge of biomolecule to exert a localized bond-rupture force and measure the biomolecule response.

Single-molecule rupture dynamics on multidimensional landscapes.

We explore emergent effects of multidimensionality of the free energy landscape on single-molecule kinetics under constant force. The proposed minimal model reveals the existence of a spectrum of unusual scenarios for the force-dependent lifetime, all of which are shown to occur on a free energy landscape with a single transition state. We present an analytical solution that governs single-molecule responses to a constant force and relates them to microscopic parameters of the system.

Theory, analysis, and interpretation of single-molecule force spectroscopy experiments.

Dynamic force spectroscopy probes the kinetic and thermodynamic properties of single molecules and molecular assemblies. Here, we propose a simple procedure to extract kinetic information from such experiments. The cornerstone of our method is a transformation of the rupture-force histograms obtained at different force-loading rates into the force-dependent lifetimes measurable in constant-force experiments.

Pulling direction as a reaction coordinate for the mechanical unfolding of single molecules.

The folding and unfolding kinetics of single molecules, such as proteins or nucleic acids, can be explored by mechanical pulling experiments. Determining intrinsic kinetic information, at zero stretching force, usually requires an extrapolation by fitting a theoretical model. Here, we apply a recent theoretical approach describing molecular rupture in the presence of force to unfolding kinetic data obtained from coarse-grained simulations of ubiquitin.

Extracting kinetics from single-molecule force spectroscopy: nanopore unzipping of DNA hairpins.

Single-molecule force experiments provide powerful new tools to explore biomolecular interactions. Here, we describe a systematic procedure for extracting kinetic information from force-spectroscopy experiments, and apply it to nanopore unzipping of individual DNA hairpins. Two types of measurements are considered: unzipping at constant voltage, and unzipping at constant voltage-ramp speeds.

Mean time-of-flight of photons in transillumination measurements of optically anisotropic tissue with an inclusion.

We study the effect of optical anisotropy on the mean time-of-flight of photons in a slab of turbid medium containing an inclusion whose optical properties differ from those of the bulk. For this analysis the difference in the mean time for a photon introduced into the slab to reach a specified target point with and without the inclusion is calculated. This difference is defined to be a measure of the contrast.

Time-dependent diffusion coefficients in periodic porous materials.

We derive an approximate solution for the Laplace transform of the time-dependent diffusion coefficient, D(t), of a molecule diffusing in a periodic porous material. In our model, the material is represented by a simple cubic lattice of identical cubic cavities filled with a solvent and connected by small circular apertures in otherwise reflecting cavity walls, the thickness of which can be neglected. The solution describes the decrease of D(t) from its initial value, D(0) = D, where D is the diffusion constant in the free solvent, to its asymptotic value, D(infinity) = D(eff), which is much smaller than D.

Time-dependent rate coefficients for diffusion-influenced reactions with centrosymmetric potentials.

Simple closed-form expressions are presented for the time-dependent rate coefficients of diffusion-influenced reactions in the presence of spherically symmetric potentials. For diffusion-controlled contact reactions, our expression reproduces the first two terms in both the short- and long-time expansions of the rate coefficient. At intermediate times, agreement with numerical results for the Debye-Hückel potential is found to be within a few percent for a wide range of parameters.

Intrinsic rates and activation free energies from single-molecule pulling experiments.

We present a unified framework for extracting kinetic information from single-molecule pulling experiments at constant force or constant pulling speed. Our procedure provides estimates of not only (i) the intrinsic rate coefficient and (ii) the location of the transition state but also (iii) the free energy of activation. By analyzing simulated data, we show that the resulting rates of force-induced rupture are significantly more reliable than those obtained by the widely used approach based on Bell's formula.

Global analysis of X-chromosome dosage compensation.

Background: Drosophila melanogaster females have two X chromosomes and two autosome sets (XX;AA), while males have a single X chromosome and two autosome sets (X;AA). Drosophila male somatic cells compensate for a single copy of the X chromosome by deploying male-specific-lethal (MSL) complexes that increase transcription from the X chromosome. Male germ cells lack MSL complexes, indicating that either germline X-chromosome dosage compensation is MSL-independent, or that germ cells do not carry out dosage compensation.

Estimation of anisotropic optical parameters of tissue in a slab geometry.

The scattering and absorption coefficients of many homogeneous biological tissues such as muscle, skin, white matter in the brain, and dentin are often anisotropically oriented with respect to their bounding interface. In consequence the curves of equal intensity of re-emitted light on the surface of the slab will no longer be circular. We here consider the problem of determining the parameters allowing one to estimate the angles defining anisotropy, directional bias of diffusive spreading, and scattering and absorbing coefficients from data obtained from time-gated measurements of light intensity transmitted through a slab of the tissue.